Wednesday, April 10, 2013

Nuthin' but a 'g' thang

I had a professor at Michigan who always thought in pictures. He would much rather draw a graph than write down a system of equations. As he drew the curves on the board, he would say "OK, here is the thing, and it touches this thing, and they go like this." And that would be it! And I would be sitting there scratching my head and thinking "OK, now are you going to tell us what you just did?" Because I've always been the exact opposite kind of guy; I would rather write down equations and define words for everything. Rarely do I think in pictures. On IQ tests, I do much worse on the "visual" sections.

Over the course of my academic existence, I've often observed this dichotomy. You have the Einstein-type people who seem to visualize everything, and then you have the Heisenberg-type people would would rather use the symbols. So I've always had the intuitive hypothesis that there are different types of intelligence; that different people tend to process information in different ways, whether due to habit or nature.

But then there are all those people who say that intelligence can be boiled down to a single factor, the mysterious "g" (which I assume stands for either "general intelligence" or "gangsta"). Since this went against years of casual observation, I was somewhat pleased to see the eminent Cosma Shalizi write an essay debunking the notion of "g". But then I saw this blog post defending the notion of "g", and claiming that Shalizi makes a bunch of errors. Basically, the disagreement revolves around the question of why most or all psychometric tests and tasks seem positively correlated with each other. Shalizi points out that this correlation structure will naturally lead to the emergence of a "g"-like factor, even if one doesn't really exist; his opponent points out that if no "g" exists, it should be possible to design uncorrelated psychometric tests, which so far has proven extremely difficult to do.

The latter post, by a pseudonymous blogger calling himself "Dalliard", contains a bunch of references to psychometric research that I don't know about and have neither the time nor the will to evaluate, so I'm a bit stumped. Normally I'd leave the matter at that, shrug, and go read something else, but I realized that my intuitive hypothesis about intelligence didn't really seem to be explicitly stated in either of the posts. So I thought I'd explain my conjecture about how intelligence works.

In a nutshell, it's this: What if there are multiple "g's"?

Suppose that simple mental tasks (of the kind apparently used in all psychometric tests) can be performed by a number of different but highly substitutable mental systems. In other words, suppose that any simple information-processing task can be solved using spatial modeling, or solved using symbolic modeling, or solved using some combination of the two. That would result in a positive correlation between all simple information-processing tasks, without any dependence between the two mental abilities.

Let's illustrate this with a simple mathematical example. Suppose the performances of subject i on tests m and n are given by:

Here, X and Y are two different cognitive abilities. b and c are positive constants. Assume X and Y are uncorrelated, and assume e, the error term, is uncorrelated across tests and across individuals.

In this case, assessing the covariance of performances across two tests m and n across a pooled sample of subjects, we will have:

Cov(P_m, P_n) = b_m * b_n * Var(X) + c_m * c_n * Var(Y) > 0

So even though the two cognitive abilities are uncorrelated (i.e. there is no true, unique “g”), all tests are positively correlated, and thus a “g”-type factor can be extracted for any set of tests.

Now suppose that by luck, we did manage to find "pure" tests for the X and Y. In other words:

P_xi = a + b_x * X_i + e_xi
P_yi = a + c_y * Y_i + e_yi

These tests would have no correlation with each other. But they would have positive correlations with every other test in our (large) battery of tests! So the "positive manifold" (psychometricians' name for the all-positive correlation structure between tests) would still hold, with the one zero-correlation pair attributed to statistical error. Only if we found a whole bunch of tests that each depended only one X or only on Y could we separate the "single g" model from the "two g" model. But doing that would be really hard, especially because in general test-makers try to make the various tests in a battery different from each other, not similar.

Notice that all I need for my "two-g" model to fit the data is that most of the b and c coefficients are nonzero and positive. It makes sense they'd all be positive; more of some mental ability should never hurt when trying to do some task. And the "nonzero" part comes from the conjecture that simple mental tasks can be performed by a number of different, substitutable systems. (Note: the functional form I chose has the two abilities be perfect substitutes, but that is not necessary for the result to hold, as you can easily check.)

Update: A commenter reminds me of the time Richard Feynman discovered that while he counted numbers by internally reciting the numbers to himself, his friend counted by visualizing pictures of the numbers scrolling by. This is the kind of thing I'm thinking of.

So anyway, there's my proposed model of basic intelligence. For those of you who didn't follow it, just imagine several dozen hyperplanes, and project them all onto one hyperplane... ;-)

An addendum: Why do people care whether there is one "g" or several? According to "Dalliard", the notion of multiple types of intelligence is attractive because it suggests that "that everybody could be intelligent in some way." Well, if that's what you want, then realize this: It's true! Remember that psychometric tests are simple mental tasks, but most of the mental tasks we do are complex, like computer programming or chess or writing. And for those tasks, learning and practice matter as much as innate skill, or more (for example, see this study about the neurology of chess players). Therefore, everyone can be "smart" in some way, if "smart" means "good at some complex mental task". Which, in adult American society, it typically does. So don't worry, America: We're all stupid in most of the ways that matter.

...Wait, that didn't come out right...

(Final note: Looking through "Dalliard's" blog, I see that most of it is an attempt to prove that black people are dumber than white people. Sigh. Depressing but hardly surprising. Needless to say, the fact that I addressed a "Dalliard" blog post is not intended as an endorsement of his views or his general interests...)

Update: A commenter points out that Dalliard's post does consider a theory similar to the one I outline here, which he calls the "sampling" theory. Dalliard cites some fairly weak arguments against the theory by someone from long ago, but recognizes that these arguments are weak. Dalliard also makes a good point, which is that for many applications - say, separating kids into classes based on test-taking skill - it doesn't matter whether there is one "g" or many.

Could you not use school results as a sample set for this kind of examination? Obviously a number of subjects are probably tapping 'creativity' or suchlike, not necessarily 'g', but even within maths I was always bad at statistics and good at mechanics. Small sample pool there, granted, but surely that's got to prove something. Surely.

Your anecdote reminds me of a story in one of Richard Feynman's books about counting. In it he discovers that while he counts by hearing the numbers in his head, his friend counted by seeing the numbers pass by as if they were on a tape. As a result, Feynman couldn't count while involved in auditory tasks like talking, but his friend could. On the other hand, the friend couldn't count while involved in visual tasks like reading, but Feynman had no problem with that.

It's a story of two very different thought processes being used to complete the same simple task. They may even seem identical to an outside observer who never bothers to ask how the person did the task in their head. In some ways, they're perfect substitutes, but they have different effects when this simple task is combined with others.

Stephen Pinkers fifteen year old book "How The Mind Works" remains a good introduction to the modularity of the mind. Dominant functions, like speech or calculation, tend to occur in specific brain regions. When these regions are damaged the nearer brain regions can shift or share these functions. In the absence most areas tend to have regular functions but it is not absolute, there is a distribution.

Schools like Eagle Hill School in Greenwich Connecticut have built their pedagogy around the insight. They have a diagnostic program where they identify physically where in a child's brain a dysfunction is occurring, usually by simply looking where the expressed dysfunction is normally executed. Once they identify the area of the problem they design a teaching program to help adjoining areas pick up the defective function.

This only works for kids below about 15, after that, brain structure seems to harden. But for kids diagnosed young, they can enter the school with major impairments and leave several years latter to re-enter normal schooling as if there was never a problem.

"Dalliard's" argument against the idea is that different tasks that have high 'g' loadings seem to be very different from each other. I don't really see how that's a convincing counterargument.

But the point about levels of analysis is right. If we just want to separate, say, kids into groups based on who will do better on tests (which I think is a useful thing to do), then you don't need to know if there is one 'g' or many.

"'Dalliard's' argument against the idea is that different tasks that have high 'g' loadings seem to be very different from each other. I don't really see how that's a convincing counterargument."

I dunno. At this point the debate becomes unavoidably normative--why do we care about "g," if it does exist? To use his height analogy, if we care about height because we need to know who can reach high shelves, then it doesn't matter whether that height is the result of long legs or long torsos. By contrast, if we care about height because people with long legs run faster, then we should pay attention to whether people have long legs rather than whether they are overall tall.

Analogously, if we care about g because most of the actual societally worthwhile intellectual tasks are some amalgam of "sub-g" faculties, then g is a useful construct. Conversely, if societally worthwhile intellectually useful tasks are correlated with only a subset of the sub-g faculties, then g is less useful.

The linked post appears to be arguing for the former. However, the argument isn't especially convincing since all of his examples are by definition artificial tests rather than real world tasks, and thus his argument doesn't have much normative oomph for why we as a society should value g as a useful analytic construct. Regardless, he does seem to have Shalizi (and you=D) dead to rights on the purely formal point that the ability to disaggregate g doesn't defeat it.

At this point the debate becomes unavoidably normative--why do we care about "g," if it does exist? To use his height analogy, if we care about height because we need to know who can reach high shelves, then it doesn't matter whether that height is the result of long legs or long torsos. By contrast, if we care about height because people with long legs run faster, then we should pay attention to whether people have long legs rather than whether they are overall tall.

Yep. That was his point about "levels of analysis"...what do we actually want to use the measure for?

What I want, of course, is smart-ification technology. So for that purpose, the question of "What is g?" is crucially important.

Analogously, if we care about g because most of the actual societally worthwhile intellectual tasks are some amalgam of "sub-g" faculties, then g is a useful construct.

Oh...well as for that, I'm convinced that most of the tasks society needs are complex tasks like computer programming and writing, not simple tasks like completing a sequence of 5 integers. Which means that technologies to increase "g" (or the multiple g's) will help people learn the useful stuff quicker, but we'll still need to teach people the stuff.

Regardless, he does seem to have Shalizi (and you=D) dead to rights on the purely formal point that the ability to disaggregate g doesn't defeat it.

But I don't think the point is to "defeat it". The point is to figure out what's going on. At least, for me, that's the point.

I think you're conflating learning styles/preferences with intelligence, which can be seen as a common, primary outcome of interest. Isolating visual learning styles etc is probably really useful for educational research and working out teaching styles, but not so much for measuring aptitude for success. It's like taking a wealth measure and arguing that it's imperfect because it doesn't account for that fact that people get their wealth from different kinds of jobs: true, but basically beside the point.

Anonymous's analogy about "total height for shelves, leg height for running" makes sense in theory, but the problem is, we still haven't found a test that can even distinguish leg height from total height, let alone found specific situations where one is more important to have.

Until then, "g" seems to cover the gamut. It's definitely theoretically possible there are uncorrelated constructs that lead to correlated tests (and a really interesting way of looking at it), but until we find real-world instances where they don't correlate, rule of parsimony says go with "g".

Different people have different styles of learning. In addition to the spatial/symbolic divide you mention, I've found that some folks are better at processing new information visually (including reading) than aurally, and some are the other way around.

I wonder how general this sort of observation is - I've noticed casually that most of these anecdotes revolve around math in some way(fwiw, and this is a very crude and inexact description, I can manipulate numbers in my head fairly easily by breaking large and difficult numbers up into smaller, more tractable chunks, and doing a series of operations on them. This may or may not have anything to do with how I was taught math at an impressionable age using blocks. I "see" numbers as objects rather than as symbols.) Would it also apply to, say, learning languages, or carpentry?

I find myself thinking of the story about the kid who immigrated from France to the USA during his education, and as an adult (and a scientist) still did his arithmetic in French and his calculus in English.

Perhaps therefore the difference between the two ways of thinking is what method you're exposed to the first time you really grapple with the topic (or what method you carried over from your previous learning, if you're inventing a new topic). Obviously it's not quite that simple, as some methods of thinking have particular benefits, there's a reason for example that people slowly invented symbolic algebra rather than just drew graphs for maths all the time, aka the Ancient Greeks.

Imagine if a wealthy person said, what is all this nonsense about "income inequality"? Don't you know that in the most important respects, we are all equal? And that the most important things in life are free? So stop your bellyaching about income inequality! Of course that would be a convenient argument for the wealthy, and we can see why they would make it. And for the intelligent, denying intelligence inequality is likewise convenient. For instance, the blogger says, "I'm convinced that most of the tasks society needs are complex tasks like computer programming and writing." Actually, most of the tasks society needs are closer to "shmearing cream cheese on a bagel." And many people have trouble doing what that takes, because they have trouble mastering things like "showing up for work on time." Sure, there may be different intelligences, but for the most important things, general intelligence is what matters, not being able to visualize numbers as colors of the rainbow. And just as income inequality is important, so is intelligence inequality. Of course, we already have effective smartification technologies to remedy this inequality. But these smartification technologies are usually some form of the socialism of behavior known as middle class morality, which is so boorrriingg, especially for smart people who don't need that sort of thing.

>> these smartification technologies are usually some form of the socialism of behavior known as middle class morality

Or effectively funded universal education. Or universal early-age nutrition. Or the creation of stable environments by a shared sense of common purpose rather than a ruthless, Social Darwinian commitment to one above all.

Oh please. The US has richly funded public education. Urban districts quite often spend more. (For example, my suburban Seattle district spends a couple thousands dollars less per student than the Seattle schools.) Washington DC is probably the most expensive large district in the nation, spending in the high teens per student annually ... and is not known for its impressive results. Equal funding for all students is fine by me. (It would force a bunch of bloated big districts to lay off edu-blob bureaucrats.) But it would do nothing but highlight how much "good schools" simply means good students, from good parents.

Food is cheap in America, this is a nation where the poor people are fat, unprecedented in human history. The fast food everyone decries--say a hamburger--has plenty of calories and protein for proper development. The very early age nutrition is obviously breast milk. Yes, more poor women should breast feed. But nutrition is not the problem.

Stable environments are created by ... parents. The state is not going to love you like your parents. It *can not* love you like your parents can. It can not create"stability" amid social wreckage--other than perhaps the "stability" of the orphanage.

I agree on shared common purpose, but this is something that comes from religion and culture--things that allow people to actually belong, that give their lives meaning and purpose. The left has made nothing but war on them. For instance currently--in evil co-operation with the cheap labor lobby--pushing amnesty to further destroy the whole concept of an American nation with an "American people". With utter contempt for the very idea of a people, a nation, I don't know exactly what the leftist "a shared sense of common purpose" is ... other than buzz words to allow a bunch of petty totalitarian bureaucrats bossing everyone around. Yuck.

Our problem is hardly "social darwinism", that's laughable.Our problem is we've seen the rise of a giant WallStreet-Washington rent-seeking, parasitic blob--finance, lawyering, lobbying, bureaucrats, journo-hacks, welfare, grantees, academic hacks--that sucks up the hard work of the ever shrinking fraction of hard working, actually productive Americans... while holding them in contempt and seeking to destroy their nation.

As to intelligence, it's mostly--over half--flat out genetic. (If you don't think so, then you must think evolution somehow "stopped working" precisely when humans created environments where "success"--and hence reproduction--was ever more heavily based on intelligently navigating a more complex environment (agriculture, trade, civilization, written language, money, bureaucracy ...) This idea is simply ludicrous and non-scientific. Almost all human evolution and selection the last 20,000 or so years has precisely been in mental traits--intelligence, conscientiousness, time-preference, cooperation, etc. And with environments changing so fast it's been evolution on steroids.

But now rather than "social darwinism" (laughable--get a clue!) we have something like the reverse. The traditional "social darwinism" that gave a strong reproductive advantage to the intelligent and well behaved enabling us to become smarter and more cooperative and create this highly productive and prosperous society ... is gone. Welfare and feminism have rolled it back. College educated women have *fewer* children than the poor. And due to our hostile elites we're topping that by flooding the nation with less intelligent (and sometimes hostile) foreign peoples. Of course when that results in yet more poverty and inequality--along with crappy schools and slow growth--someone will shout about "educational equity" and "nutrition" and "social darwinism".

James Flynn noted that measured "g" steadily increased over time across all measured populations. He attributed this to greater familiarity with abstract reasoning, which kind of supports your point - lower g was not less intelligence, but less of a particular kind of intelligence (the kind than can be captured by written tests). As to whether more of this is good - that depends on how the environment goes. We may come to value carpenters more than software designers.

These findings are consistent with the measurement invariance model. Using MGCFA to test MI model, some dutch researchers showed that IQ scores are not comparable across cohort, because the g scores at earlier time is not the same as later time. This means that those IQ gains were hollow, the Flynn Effect thus being "empty" gains.

See, Are intelligence tests measurement invariant over time? Investigating the nature of the Flynn effect, Wicherts 2004.Comparability of IQ Scores over Time, Must 2009.

Regarding Noah's post, I will point to Jensen's book, The g Factor, specifically pages 130-132, 259-261. See here. Nothing of what is said above is inconsistent with the g model.

Error and nonsense. Forget the above. I will rephrase it : "IQ differences across cohorts are not reflecting the same underlying construct, that is, are not explained by a difference in common factors".

I have a friend in my econ grad program (we take all the same classes), and the ones that I find easy to follow and intuitive she thinks are an organizational train wreck, while the ones that I sit in the back and read because I have no chance of following, she easily follows and understands. It seems like our intuition engines are entirely opposite.

I too was a very logic-minded student. I was a math major in college before switching to philosophy and my graduate school emphasis was in what is sometimes called "philosophical logic" - lots of use of symbolic techniques, with rigorous argumentation, theorem proving, metatheory, etc.

Later in life I grew embarrassed that I could barely draw at all. If I tried to draw something, the results looked like something a small (graphically incompetent) child might have produced. So I decided to learn how to draw. I never got very good at it, but I did get much, much better.

Drawing obviously takes intelligence. We recognize the people who do it well as having a certain kind of genius, and we think of the first appearance of drawing in the historical record as indicating a new level of cognitive advancement. But I can't think of any intelligence test I ever took that tests the kinds of cognitive skills I was trying to acquire when I was learning to draw. Nor do I know exactly how one would test them. Intelligence tests focus on skills for whose outputs their are usually very simple objective standards measuring the output on only a single dimension. You query the subject, they give you an answer, and you can then assign a simple "correct" or "incorrect" label to the answer. But even if you think of drawing as not the production of something with "artistic value" but as a skill that aims at faithful representation, there are very many ways in which a drawing might and might not represent its object (and the experience of seeing that object) well - color or value, proportion, perspective, appropriate focus on the most salient details - and they deviate from the "ideal" along several sometimes competing dimensions. Some drawings use a very small number of representational elements but strike the viewer as having a great deal of verisimilitude, while others are full of locally faithful details but are global failures.

I came into econ-grad school preferring equations and by the end of the first year, I'd come around to thinking that graphs were the way to go. One of my closes friends, who prided himself on having been admitted to the program with the lowest math-GRE score in its history (this was about 30 years ago), journeyed in the opposite direction.

So long as we say that "intelligence" is what we measure when we take intelligence tests, we end up only talking about a pocket universe of test taking. This would be okay if G correlated with real-world accomplishment, and it often does, but not always. (And by accomplishment, I mean accomplishing what the person wants to accomplish, not his ability to fit some externally imposed role.)

The stereotype is the roomful of Mensa geniuses, basking in their brilliance before taking the last bus home to their mom's basement. The opposite stereotype is the roomful of wildly successful business or government types, thick as two planks, trading conventional wisdom sound bites before going home to a 3 acre mansion, a fancy dinner, and general public acclaim.

Intelligence isn't quite the word for the ability to accomplish. Lots of it can be luck, but persistence, sociability, inborn vigor and high energy levels, bloodymindedness, and the ability to self-motivate seem to be more important than pure G intelligence. If only we could increase THOSE!

"The stereotype is the roomful of Mensa geniuses, basking in their brilliance before taking the last bus home to their mom's basement. The opposite stereotype is the roomful of wildly successful business or government types, thick as two planks, trading conventional wisdom sound bites before going home to a 3 acre mansion, a fancy dinner, and general public acclaim."

For those stereotypes to be of any use, they have to be based somewhat in reality. My experience has been that sheer intelligence can get you a minimum of a comfortable middle-class lifestyle. Maybe if you're in the top 1% in sociability, you could also get there without much else if you choose the right profession. Persistence/vigor/high energy level/self-motivation/bloodymindedness (really all descriptions of the same thing) but with poor intelligence and sociability in our current economy? Good luck, man.

"For those stereotypes to be of any use, they have to be based somewhat in reality. My experience has been that sheer intelligence can get you a minimum of a comfortable middle-class lifestyle. Maybe if you're in the top 1% in sociability, you could also get there without much else if you choose the right profession. Persistence/vigor/high energy level/self-motivation/bloodymindedness (really all descriptions of the same thing) but with poor intelligence and sociability in our current economy? Good luck, man."

The correlation between IQ and income ranges from as low as 0.06 to as high as 0.15There are plenty of *relatively* poor geniuses out there.

" Lots of it can be luck, but persistence, sociability, inborn vigor and high energy levels, bloodymindedness, and the ability to self-motivate seem to be more important than pure G intelligence. If only we could increase THOSE!"

You want more "bloodymindedness"? Could be translated as "stubbornness" - but also "ruthlessness". I'm not sure that ability to climb heirarchies (i.e. success) translates exactly into productiveness. Some great people in history, were at the time unsucessful.

"Update: A commenter points out that Dalliard's post does consider a theory similar to the one I outline here, which he calls the "sampling" theory."

Se-ri-ous-ly?

Slowly -- kicking, screaming ("Racist!") and trying to reach out for things -- Noah Smith and other "progressive people" are being dragged to something more like Jensen & Rushton's position. Of course -- as progressives cannot bring themselves to READ "racist" authors like these -- they are bound to rediscover the weel now and then.

I would say it's something different. We've all known since we were 10 years old that some people are smarter than others; that's far from a revelation. The question of whether some smart people think in a fundamentally different way than others is an interesting question that guys like Jensen and Rushton generally ignore, in their eagerness to prove what everyone already knows (i.e. that some people are smarter than others).

They also focus on race, which is a complete distraction. Who cares if, say, Korean people are on average smarter than Irish people? Since IQ tests are so easy to administer, observing whether someone is Korean or Irish is of no additional help in predicting their mental abilities (you get that, right?). Just give them an IQ test.

So all the focus on race is pointless, and smacks of an ulterior motive...guys like "Dalliard" and Steve Sailer just want to keep black guys from banging their daughters & girlfriends.

Continuing to construct yet more IQ tests is a pointless endeavor anyway. We've done plenty of that. What we need is to discover the physiological mechanisms of intelligence, so we can boost it with technology. That is what Steve Hsu is starting to do. But that is something that Jensen, Rushton, etc. apparently lack either the IQ, or the complex learned skills, to do...so they keep just doing statistics on more and more pencil-and-paper IQ tests. ;-)

I think you are being a little unfair with Arthur Jensen and Phillippe Rushton. They were pioneers in intelligence research and as such had to work with the tools they had (statistics, reaction times, IQ tests, etc). Hsu is a great guy, but don't forget that cheap DNA sequencing is something from the last ten years. And some of the groundbreaking study in this area (v.g. genome-wide complex trait analysis, "Visscher Program"*, etc.) build upon Jensen & cia. They CITE Jensen & Cia., for God's sake! Do not let your "liberal creationism"** stand in the way of pursuit of truth and basic civility.

* Term coined by Turkheimer to designate because "[h]isname appears in one role or another on practically every paper that has been published on the topic" (see: http://people.virginia.edu/~ent3c/papers2/StillMissingFinal.pdf)

** Term coined by Slate's William Saletan to designate dogmatic faith in "equality of intelligence" between human groups (see: http://www.slate.com/articles/health_and_science/human_nature/features/2007/created_equal/liberalcreationism.html)

As it stands, a lot of social policy in the United States and other nations is based on implicit assumptions that all groups of people are innately equal in psychological traits. Unequal outcomes is treated as de-facto proof of invidious discrimination and a legacy of oppression. Policies are implemented that attempt to rectify these inequalities and the result has been systematic state-enforced discrimination against higher-performing groups, burdensome taxation and laws preventing the right to freedom of association. False beliefs lead to bad policy.

Do not let your "liberal creationism"** stand in the way of pursuit of truth and basic civility

Oh, basic civility is right out. This is blog-land...and the comment section of blog-land no less...The gloves are off! ;-)

The "liberal creationism" thing kind of reveals that the concern over "race and IQ" is just politics.

As it stands, a lot of social policy in the United States and other nations is based on implicit assumptions that all groups of people are innately equal in psychological traits.

I don't think that's true.

Unequal outcomes is treated as de-facto proof of invidious discrimination and a legacy of oppression.

Well that is bullshit, certainly. But you don't need to prove that black people are dumber than white people to see that "unequal outcomes" is a bad guide to policy.

burdensome taxation and laws preventing the right to freedom of association.

Ahh, you're sort of giving away the game here, aren't you? ;-)

"Don't make us let the black people in our restaurants! We're just keeping them out because their group on average has lower IQs! It's not because we're afraid of them beating us up or having sex with our daughters or anything!"

Nah, I've read Sailer. It's pure mind-poison. The man just repeats conventional ideas over and over, occasionally with some evidence, most often without, and it has the effect of seeping in and coloring your worldview. After a few weeks of reading Sailer, I had to go purify my mind by reading a bunch of Japanaese "Nihonjinron" right-wing race theory. The total contradiction of the two stylistically similar worldviews clarified how much bullshit there is in conventional wisdom.

"Well that is bullshit, certainly. But you don't need to prove that black people are dumber than white people to see that "unequal outcomes" is a bad guide to policy."

Actually you hear arguments like this *all-the-time*. You could probably google the phrase "achievement gaps" if you're not just playing the fool. In addition, much of the "77 cents on the dollar" and other feminist claims are based on this argument.

"Nah, I've read Sailer. It's pure mind-poison. The man just repeats conventional ideas over and over, occasionally with some evidence, most often without, and it has the effect of seeping in and coloring your worldview. After a few weeks of reading Sailer, I had to go purify my mind by reading a bunch of Japanaese "Nihonjinron" right-wing race theory. The total contradiction of the two stylistically similar worldviews clarified how much bullshit there is in conventional wisdom."

"liberal creationism" is just another term for "I don't like it". Not to put too fine a point on it, Saletan is an idiot. He may be an intelligent idiot; I neither know, nor care, but he's a Procrustean just as much as the people he presumes to criticize there. He crams them into a little box of his own defining, trims off anything that happens to stick messily out, slaps a neat little label on it, and thinks he's done a Good Thing. Is he a "Liberal"? I suppose it depends who's doing the defining. Does it matter? There are people who get more pleasure from kicking their supposed friends in the crotch than their supposed enemies (does the name Lieberman ring a bell?). Saletan has (when I've paid much attention to him) seemed to fall more or less into that camp. The fault may be mine in that his writing irritates me sufficiently that I may miss whatever point he is struggling to make. If so, my loss. I figure life's too short to read idiots when there are so many interesting and insightful people I have barely started to work on. Incidentally, my blood type is the same as my motto for life: "Beer and Donuts make life worth living"*

At least in this instance, I think Saletan's only sin was preaching against his own “tribe”. Jonathan Haidt (ex-card-carrying Democrat) have already noted the pernicious effect of tribalism in the Ivory Tower*, and presciently wrote three years ago:

http://www.edge.org/response-detail/10376

“FASTER EVOLUTION MEANS MORE ETHNIC DIFFERENCES

The most offensive idea in all of science for the last 40 years is the possibility that behavioral differences between racial and ethnic groups have some genetic basis. Knowing nothing but the long-term offensiveness of this idea, a betting person would have to predict that as we decode the genomes of people around the world, we're going to find deeper differences than most scientists now expect. Expectations, after all, are not based purely on current evidence; they are biased, even if only slightly, by the gut feelings of the researchers, and those gut feelings include disgust toward racism. (...)

Skin color has no moral significance, but traits that led to Darwinian success in one of the many new niches and occupations of Holocene life — traits such as collectivism, clannishness, aggressiveness, docility, or the ability to delay gratification — are often seen as virtues or vices. Virtues are acquired slowly, by practice within a cultural context, but the discovery that there might be ethnically-linked genetic variations in the ease with which people can acquire specific virtues is — and this is my prediction — going to be a "game changing" scientific event. (By "ethnic" I mean any group of people who believe they share common descent, actually do share common descent, and that descent involved at least 500 years of a sustained selection pressure, such as sheep herding, rice farming, exposure to malaria, or a caste-based social order, which favored some heritable behavioral predispositions and not others.)

I believe that the "Bell Curve" wars of the 1990s, over race differences in intelligence, will seem genteel and short-lived compared to the coming arguments over ethnic differences in moralized traits. I predict that this "war" will break out between 2012 and 2017.”

"After a few weeks of reading Sailer, I had to go purify my mind by reading a bunch of Japanaese "Nihonjinron" right-wing race theory."

OK, you piqued my curiosity. Is there a synopsis some where?

Anyway, I get a kick out of Sailor and his type. He implicitly assumes that whatever attributes that his tribe stereotypically has is superior and everyone else's is inferior (and that his tribe has them in abundance; and ignores culture). Of course, I could play the same game and say the same thing (or, even more fun, find data that shows that Sailor's Peeps are actually not superior at all).

Are there hypothetical tests like the ones Noah mentioned that don't correlate with each other but do correlate with other tests? My understanding is that there are not.

Peter T, my recollection is that Flynn noted the rise in IQ scores early, but doesn't think they constitute increases in g.

Noni Mausa, as you note, g is predictive. In pretty much everything except facial recognition & sense of rhythm as skills, and occupations other than vegetable picking. You are, however, correct that personality traits are important. My understanding is that most of the ones measured aren't as predictive as IQ (or even how distinguishable "executive function" is from IQ) though.

Actually, there is rather a lot of evidence that personality traits do predict success in life. Personality traits are a bit more malleable than IQ, especially in early age intervention, and the effects do not seem to fade out as entirely during adulthood as the IQ effects of early intervention.

James Heckman does a lot of work on the effects and ROI of early intervention. The results are very encouraging.

Here is a recent - April 15, 2013 - paper by Gensowski, reanalyzing the Terman study of high IQ people born in the early 1920's. I'm unable to critique the analysis methods used; they *sound* good to me. http://home.uchicago.edu/~mgensowski/research/Terman/Terman.pdf

Gensowski shows that, for this cohort, men who were extroverted, conscientious and less agreeable were likely to earn more. Even for this very high IQ cohort of men, higher IQ meant greater success.

There is a lot of recent research on the topic of personality traits and success. I just picked yesterday's paper because it's fun to cite something so recent.

Noah Smith said:Final note: Looking through "Dalliard's" blog, I see that most of it is an attempt to prove that black people are dumber than white people. Sigh. Depressing but hardly surprising.

Depressing as the matter may be, it is a topic that merits inquiry and dispassionate analysis, and I'm of the opinion that the contributors to the Human Varieties (HV) blog have been doing a commendable job of it. HV contributor johnfuerst wrote a great post on his other blog summarizing why the hereditarian hypothesis is the most parsimonious explanation for black/white differences in cognitive ability. I'd recommend anyone who is curious about the subject matter read it.

Depressing as the matter may be, it is a topic that merits inquiry and dispassionate analysis

Why?

Suppose you want to tell who is smarter, me or Shaquille O'Neal. You give us both IQ tests; he gets a 139, I get a 142. How could the knowledge that he's black and I'm white possibly add any information to the test result???

It matters because our system has features that take black and white (affirmative action, networks & cultural stuff) into account and knowing the broad characteristics of people with those features helps you make predictions.

Once again: it also matters from an human development & economic point of view because what is "efficient" to do depends *a lot* on mean IQ. If your mean IQ is low, there are a lot of gains to be had from things that change that, i.e. a classic malnourishment vs. famine type problem. China is unlikely to benefit from nutrient fortification in the same way Africa will.

It also matters for detecting the presence of discrimination.

The lack of legendary female achievement in mathematics/engineering/music/technology (notwithstanding Noether, Curie, etc.) on par with men would be extremely disturbing (are we living in a subtle handmaiden's tale?) if it weren't for the fact that men are more object oriented than women from birth (hence receive more pleasure than women in their technical exploits, on average of course) and also have higher standard deviations in their intelligences (more geniuses and also more cases of down's syndrome/aspergers/autism/anti-sociality/mental illness in general/strange sexual behavior/straight up criminals). I wouldn't surprised if a more sophisticated intelligence (2 g's!!!) theory discovered similar things about the differences between blacks and whites. Of course, the thing to do know is that the color itself is arbitrary and just a proxy for genetics and ought to decrease in importance over the next century.

Of course, Shalizi comes from the right place and is correct that g is an empty theory in the sense that it doesn't help us work on AI, but for humans, it's still useful.

Group IQ matters a ton for thinking about the intersection of I/O econ and immigration policy. Do we really want the kind of I/O that accompanies millions of illegal immigrants? Unlike the above, this isn't baiting. There's almost no question that crime would increase without discriminative stop-and-frisk policies, but I could see welfare considerations for the US swinging either in favor of or against illegal immigration. But it's a discussion we can't have because economists don't think about the implications of labor mobility beyond comparative advantage, remittances and economies of scale.

Perhaps the most important discussion to be had (what will the impact be on automation rates/growth/inequality) is only being had by the guys at AEI for politically motivated reasons and by Professor Autor @ MIT

Also, think about the following fact: Just because your ideas are socially taboo doesn't mean they're not also a bunch of crap. That exciting tingly feeling of "Oooo hoo hoo, I'm thinking forbidden thoughts and tasting the elixir of banned knowledge!" might just be a total cognitive illusion...but it is an illusion that people like Steve Sailer use, intentionally or not, to repackage conventional wisdom as some kind of cutting-edge scientific findings.

Man, *practically everyone* thinks women don't make as good mathematicians and engineers as men. It's taboo to say it but almost everyone thinks it. That doesn't make it right. As a matter of fact, I *don't* think it's true! That puts me in the majority as far as social taboos are concerned, but in the tiny minority as far as actual beliefs are concerned...

To mount my hobby horse yet again, and bravely ride furiously in the same spot - we're human. We're built to make snap decisions based on whatever information we have. Stereotypes, biases, -isms and other tribalist reactions are all part of that, as is our tendency to think only in the short term and ignore or discount the obvious danger off on the horizon. Anything to let us make a quick choice without agonizing over the details. We use lots of outside confirmation to "prove" that we're right - religion, conventional wisdom, "broad characteristics of people", whatever we need to assure ourselves that we're not just rationalizing our particular prejudices. This way we even get to say, regretfully, of course, "I get minimal pleasure from the fact that my ideas .. are correct". More in sorrow than in anger, but there it is. Now, I freely admit that I could be wrong about all this - I'm not, of course, but I admit the infinitesimal, laughably unlikely chance does exist.

Sounds like the same line of argument Franz Boas destroyed in the 19th century when phrenology and craniometry were the sciences that determined that Jews were incompetent at math and science and would never be wholly human. Somehow we solved the problem of the congenitally ignorant Poles, Slavs, and Hungarians, along with the indolent and heat touched Portugese, Spaniards and Italians. Not sure if we solved the Irish problem. Fortunately all these people can pass as white and after a few generations of passing they can be as mediocre as any other American of non-English extraction excluding the hairy Welsh and the gruff and reticent Yorkshireman.And Saletan is an imbecilic writer no less than any other opinion monger; attributing any political belief to him, any credence, is like endorsing Kraft macaroni and cheeze over WEstern Family because of its brand identity.I submit to you that white people are inferior intellectually and have only triumphed over the world for their ability to lie, cheat, steal and oppress others and that IQ tests are simply another means to that end. Any inferiority attributed to any group is most easily explained through the fact that they are identified as a group and therefore can be isolated, shunned, abused and systematically repressed. Anecdotal support comes from my own mathematical career, when I was informed that as a non-Asian I would likely not pass spherical trig/precalculus. Off to advanced applied sciences where everyone had a shot I went.

I second Leon. It is crazy to believe that there is a conspiracy to defraud thousands of tests through almost one century... The objective? Make black people and other minorities look dumber than white people. This racists were so devious that, in order to hide their white supremacism, they made East Asians appear a little bit smarter, and Jews way more intelligent than the rest of the lot. They infiltrated the Nobel foundation (hence all those awards too people of ashkenazi heritage) and universities as well.

"Man, *practically everyone* thinks women don't make as good mathematicians and engineers as men. It's taboo to say it but almost everyone thinks it. That doesn't make it right. As a matter of fact, I *don't* think it's true! That puts me in the majority as far as social taboos are concerned, but in the tiny minority as far as actual beliefs are concerned..."

Ok I've chewed on this. It matters why you believe something.

At the end of the day, the only things you can believe are based on are your anecdotes, a couple good theories about evolution, and whatever empirics you can get your hands on before before you die.

If you read the IQ std. dev results, look at sex-differences in behaviors and preferences from infancy, read anthro-stuff, do research in neuro, travel around the world, and still come to this conclusion, what is the point of posting or thinking about these issues?

In the end you're going to let your prior probabilities of the relevant hypotheses overwhelm what you see in part on the basis of an assumption of bad faith in people who hold those hypotheses. Why not just go outside?

"I really don't see why we need any "dispassionate analysis" in this area. It's really not all that important, except to people who are trying to pursue invidious agendas."

At first I used to believe something like this, however these facts are important for thinking clearly about the effects of affirmative action, discriminative stop and frisk policies and "disparate impact" laws/lawsuits.

If we lived in a world that did not explicitly discriminate on the basis race with a particular policy goal in mind (countering implicit discrimination), then these facts would become less important.

I don't agree. I am a radical egalitarian, but none of the policies I support for promoting an equal society have the slightest connection with views about the innate cognitive capacities of human beings.

Skimming through the first 10 results, none of them cite The Bell Curve to primarily criticize it. The only criticism I found was in RA Gordon's article which while expressing agreement with a number of it's points, criticizes Herrnstein & Murray for under-estimating the role g plays as a causal mechanism for racial differences in socio-economic outcomes, which is essentially a criticism from the opposite direction than how it was primarily attacked in the mainstream press. I won't bother going through the next 174 papers, but since the Google results are organized around most cited articles being listed first, I think it is a pretty good example of the general trend within the psychometric literature.

***How could the knowledge that he's black and I'm white possibly add any information to the test result???***

@ Noah,

Daniel Seligman addressed this in his book 'The IQ Controversy". It's relevant to the extent that there are policies that discriminate in favour of individuals on the basis of group membership. The justification for those policies tends to be that there are statistical discrepancies.

Those discrepancies are caused by some external factor (eg. discrimination, institutional bias, terrible public schools etc). So it is morally justifiable to discriminate in favour of individuals from the underrepresented group. The Race Relations Commissioner in NZ has previously suggested exactly this.

If group disparities are a policy concern (which they clearly are in terms of education for starters) then you need to investigate causation to formulate a policy response, no? Also, it may be relevant to the moral quesstion of whether counter discrimination is justified?

***. I am a radical egalitarian, but none of the policies I support for promoting an equal society have the slightest connection with views about the innate cognitive capacities of human beings.***

@ Dan Kervick,

To promote an equal society isn't it useful to understand the causes of inequality? Utopian ideas aren't going to help anyone. Also, if you don't know the causes then the wrong factors (or people) can get blamed (eg. teachers).

Liberals like Steven Pinker and Peter Singer have written on this subject. Singer, for example points out that a 'A Darwinian Left' would not:

• Assume that all inequalities are due to discrimination, prejudice, oppression or social conditioning. Some will be, but this cannot be assumed in every case;

Notice that all I need for my "two-g" model to fit the data is that most of the b and c coefficients are nonzero and positive. It makes sense they'd all be positive; more of some mental ability should never hurt when trying to do some task.

Actually, because blood flow to different portions of the brain varies according to demand, use of one mental ability can easily mean decreased simultaneous ability in another competing for that blood flow.

"Suppose that simple mental tasks (of the kind apparently used in all psychometric tests) can be performed by a number of different but highly substitutable mental systems. In other words, suppose that any simple information-processing task can be solved using spatial modeling, or solved using symbolic modeling, or solved using some combination of the two. That would result in a positive correlation between all simple information-processing tasks, without any dependence between the two mental abilities."

There was an example in a cognitive psych book, where they were trying to figure out if they could exploit extra cognitive power by adding spatial tasks in verbal form, for people who were already spatially maxed out (pilots). The idea was that if there was specialized verbal processing power not available for spatial tasks (as opposed to general cognitive ability which was good for both), that they could get a little extra this way.

Then end result, after lengthy testing on a selected group of largely similar people for a specialized set of tasks, was 'maybe, maybe not'.

"That would result in a positive correlation between all simple information-processing tasks.."

This is merely a variant of the sampling model. For a good discussion of the main models and their limitations refer to: Van Der Maas, et al. (2006). A dynamical model of general intelligence: The positive manifold of intelligence by mutualism.

"(Final note: Looking through "Dalliard's" blog, I see that most of it is an attempt to prove that black people are dumber than white people. Sigh..."

You're being overly disingenuous, here. Number 4 on the top 10 list of social science "grand challenge questions that are both foundational and transformative" is: "How do we reduce the ‘skill gap’ between black and white people in America?" (Giles, 2011). That "skill gap" is none other than the general mental ability gap. This differential sometimes also goes under the name of the "achievement gap" (in context to education) and the "human capital gap" (in context to economics), but it's one and the same. I find it incredible that you would play the "Uh, duh" game -- but I guess I'm not overly surprised.

Now, specifically in reply to your statement, HV is not devoted to proving "that black people are dumber than white people". If "dumber" means "less generally intelligent, on average" doing so would be unbearably redundant -- since this is a well established fact -- at least if we understand "general intelligence" in terms of the positive manifold. One of the many questions which we are interested in exploring is: "Why?" And what makes our approach relatively unique is that we are willing to indulge in a behavioral genetic perspective, a perspective which is well supported -- see, for example: Rowe, D. C., & Cleveland, H. H. (1996). Academic achievement in blacks and whites: are the developmental processes similar?. Intelligence, 23(3), 205-228.

You say: "Well that is bullshit, certainly. But you don't need to prove that black people are dumber than white people to see that "unequal outcomes" is a bad guide to policy."

Again, that there is a large mean difference in general metal ability is a fact. The question is: "Why?" The first order relevance is: "This difference accounts for outcome disparities." And the second order relevance is: "Many people find these disparities to be worthy of investigation." Is this irrational of them -- and us along with? This is where I would disagree with you. If the racial intelligence gap -- which underlies most outcome disparities -- is the product of historic discrimination, as commonly thought in some quarters, than it seems reasonable to approach it differently than if it is largely the product of genetic differences (as are the gaps between arbitrarily defined populations (e.g., booger eaters versus non booger eaters), given the h^2 of g in the US). This is where the interest in the question comes from. I'm sure that if you didn't have your head so far up your ass you might, if you tried really hard, be able to recognize this. But maybe not.

A comment of mine added lately to the HV thread, that may resonate more with economists than statisticians:

Exceedingly interesting. That does make me think that the claim for unitary g must be analogous to what, in Economics, is called GARP — that is, the existence of a unitary utility function that can rationalise the test data, in the sense of Discrete Choice theory — a sort of Generalised Axiom of Revealed Intelligence.

Has there been any work along those lines? Maybe it’s time to get Hal Varian involved. I can see that if we ask ‘what is the economic value of a question on an IQ test to the individual, that theory heterogeneous variability allows them to ‘punch above their weight’ on, might be an excellent way to find distributional evidence in the data for the theory. Such situations are not only extremely rare — they are Generalised Extremely *Valuable* to the individual in question, given the economic value of the test!

Fleshing out my though a bit — it seems to me that ‘IQ’ is just voting theory turned on its side, so to speak. Suppose we have an island with 2000 people and 7 policy alternatives. We form a matrix with 7 rows and 2000 columns. Each column contains the preference (a rank from 1 to 7) of each ‘voter’. Along the right hand side, we have a social welfare function that computes the social (global island) utility of that alternative. Under suitable assumptions, there is a single voter whose preferences must mirror the social welfare function. Choosing him for dictator is superior to any voting scheme, so far as directly selecting the highest social welfare for the island is concerned.

Now, instead of making the people the columns, make them the rows — that is we have 7 people and give them a battery of IQ tests consisting of 2000 questions total. Along the right hand column, write down their true IQ score — to the ‘global intelligence’ of each of the 7 test takers in fact known, but we wish to rank the individuals without knowing it using some computation based on their answers or perhaps additional information.

For each question on each test, we can under suitable assumptions rank the value of that question, ordinal-ly, for each of the 7 individuals — and assuredly each question has economic value to them, since the higher their ‘bundle of scores’ subject to their ‘intelligence constraint’ the better adapted to life they are, which is a sort of utility. Therefore we have columns that are permutations of the numbers 1-7.

Again, under suitable assumptions, there is a single question on a single test the value of answering which exactly mimics the IQ ranking. Call it the Dictator Question. That is, IQ would seem to be a mirror of ‘ordinal social welfare’, when we think of people as ‘adaptive policy alternatives’ in an evolutionary situation, and the situations they face — modelled in tests — as the ‘individuals’. The Dictator Question plays the role of a ‘representative agent’ I guess — in the sense that a test replicating it many times would correctly model the expectations of administering a battery of tests to a population.

MBTI can help explain the fundamentally different ways in which people like to think. As an Intuitive Perceiver, like Einstein (INTP) , I naturally prefer thinking visually. A Sensing Judger would be more inclined towards the explicit mathematical thinking method.

"Now suppose that by luck, we did manage to find "pure" tests for the X and Y. In other words:

P_xi = a + b_x * X_i + e_xiP_yi = a + c_y * Y_i + e_yi"

You know very well that if you managed to find those two uncorrelated tests you could disprove g. You would partial out the correlation of P_X and a more general test and show the general test (or the first factor) is correlated to P_Y. So find the two tests.

You know very well that if you managed to find those two uncorrelated tests you could disprove g. You would partial out the correlation of P_X and a more general test and show the general test (or the first factor) is correlated to P_Y. So find the two tests.

Actually it's not so simple as my toy model. Suppose that X and Y are actually correlated at say, 0.2, because both depend on nutrition. They're still mostly distinct, in that they have different genetic and/or developmental causes, but they would actually test as somewhat correlated. I'm pretty sure tasks have been found with correlations as low as 0.2 - just looking at this table from Dalliard's blog reveals quite a few:http://humanvarietiesdotorg.files.wordpress.com/2013/03/wj-r_corr_matrix1.png

If the weak positive correlation is just due to something simple like nutrition, then we've already found tests that separate X and Y,. we just don't realize it.

So why do we care about X and Y? Because while "g" may be perfectly acceptable as an outcome measure for psychometric testing, in order to develop smartification technology we'll need to have a more fine-grained understanding of whether g is monocausal or multi-causal.

And as I see it, the purpose of all science is to create useful technology, and smartification seems to be a big unexploited area.

Over the course of my academic existence, I've often observed this dichotomy. You have the Einstein-type people who seem to visualize everything, and then you have the Heisenberg-type people would would rather use the symbols. So I've always had the intuitive hypothesis that there are different types of intelligence; that different people tend to process information in different ways, whether due to habit or nature.

Goodness me the worlds a complicated place, isnt it? How can a thing be one way, and yet another way at the same time. Its just a "buzzing and blooming confusion".

Thats why we pay smart people above average wages, so they can take all this complication and reduce it to manageable proportion, easily digestible by dummies.

"g" is not a real observable entity like a cell or a star. Its a construct whose sole purpose is to predict behaviour, in this case intelligent behaviour across a variety of domains.

"g" means people who are smarter than average at one thing (writing) will also probably be smarter than average at another thing (sums). Sort of like someone who is good at one sport (football) will likely be good at another sport (basketball).

Its worth remembering that Einstein, possessed of an unbeatable physical intuition, was no slouch at writing. And Heisneberg, the virtuoso at mathematical formalism, was also an accomplished pianist.

Of course "g" works at higher scales. Smart countries such as England and Japan, seem to be smart at a wide variety of domains, making machines, doing sums, designing vehicles and so on. This could be just cultural tradition or it could be natural incarnation. Either way the g factor is highly heritable.

This was all laid out nearly two generations ago by Jensen. And all the huffing & puffing by Gould & Cosma will not make a whit of difference. Nature cannot be fooled.

Its not that hard to figure out. But clever-silly eggheads like Cosma & Noah like to complicate things. Which prompts the question: Why? No doubt to give themselves something to do that makes them look better than bad people like Jensen, Steve Sailer & me, apparently.

"Notice that all I need for my "two-g" model to fit the data is that most of the b and c coefficients are nonzero and positive. It makes sense they'd all be positive; more of some mental ability should never hurt when trying to do some task. And the "nonzero" part comes from the conjecture that simple mental tasks can be performed by a number of different, substitutable systems. (Note: the functional form I chose has the two abilities be perfect substitutes, but that is not necessary for the result to hold, as you can easily check.)"

From what I gather, this is basically the point of "g". The assumption that an improvement in one intelligence can only improve performance on a meaningful intelligence test guarantees correlation between the intelligences. "g" just tends to be the combination of basis intelligences that has the highest correlation with scores on intelligence tests.

One could theoretically create a basis of intelligence vectors that are orthogonal to each other, but that would necessitate the existence of tests where the [b], [c], etc. vectors are orthogonal to each other (i.e. you would need some negative coefficients).

Of course, all of this assumes that we're talking about a linear system.